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(8.02-8.05)
Solve the systems of equations below using the method indicated in each part of the table. Be sure to show ALL your work for each method in order to get full points! (15 points)
Answers
The solutions to the systems of equations are:
1. (2, 3) (see attachment below). [one solution]
2. no solution
3. (3, 13) [one solution]
Solution to a System of Equations?The solution to a system of equations is the x-value and y-value that will make both equations true. It can be found either using a graph, by elimination method, or substitution method as explained below.
1. Using graph to solve y = 2x - 1 and y = 4x - 5:
The solution is the point where both lines intersect which is: (2, 3) (see attachment below). [one solution]
2. Solving using substitution method:
x = -5y + 4 ---> eqn. 1
3x + 15y = -1 ---> eqn. 2
Substitute x = -5y + 4 into eqn. 2
3(-5y + 4) + 15y = -1
-15y + 12 + 15y = -1
-15y + 15y = -1 - 12
0 = -13 (this shows that there is no solution)
3. Using elimination method:
14x = 2y + 16 ---> eqn. 1
5x = y + 2 ---> eqn. 2
1(14x = 2y + 16)
2(5x = y + 2)
14x = 2y + 16 ----> eqn. 3
10x = 2y + 4 -----> eqn. 4
Subtract
4x = 12
x = 12/4
x = 3
Substitute x = 3 into eqn. 2
5(3) = y + 2
15 = y + 2
15 - 2 = y
13 = y
y = 13
The solution is: (3, 13).
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Related Questions
A circular swimming pool has a radius of 28 ft. There is a path all the way around the pool that is 4 ft wide. A fence is going to be built around the outside edge of the pool path.
A circle has a radius of 28 feet. A larger circle goes around the smaller circle that is 4 feet wide.
About how many feet of fencing are needed to go around the pool path? Use 3.14 for Pi.
88 ft
100 ft
176 ft
201 ft
Answers
The number of feet of fencing that is needed to go around the pool path is D. 201 ft.
How to calculate the number of feet?
We have a pool with a radius of 28 feet. The radius of the outer edge of the pool path would be equal to the radius of the pool plus the width of the path.
= (28 + 4) feet
= 32 feet
The circumference of the outer edge of the pool path would be equal to the perimeter.
p = 2 * pi * r
p = 2 * 3.14 * 32
p = 200.96 feet
p = 201 feet
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41 is a prime number found in the middle of a list of 7 consecutive numbers. find the 7 consecutive numbers
Answers
Answer: 29, 31, 37, 41, 43, 47, 53.
Step-by-step explanation:
can you simplify 8/15+1/6
Answers
Answer:
Yes and the answer is 16/5
Step-by-step explanation:
Find the reciprocal of the divisor
Reciprocal of 1/6 : 6/1
Now, multiply it with the dividend
8/15 ÷ 1/6 = 8/15 × 6/1
And after that you get 48/15 but after reducing the fraction, the answer is 16/5. ( In mixed form, 3 1/5 )
I hope this helps and I am a middle school student answering this question.
Answer:
7/10Step-by-step explanation:
can you simplify 8/15+1/6
8/15 + 1/6 =
(16 + 5)/30 =
21/30 =
semplify (21:3 and 30:3)
7/10
Find the interquartile range (IQR) for the following data set: 52, 60, 24, 36, 48, 52, 72
Answers
Answer:
24
Step-by-step explanation:
The interquartile range defines the difference between the third and the first quartile.
Let's put this data set in ascending order:
24, 36, 48, 52, 52, 60, 72
The median is 52. The median of both the lower (1st quartile) and upper half (3rd quartile) of the data is 36 and 60.
Now we can subtract the first quartile from the third quartile (60 - 36) to get the interquartile range of 24.
Hope this helped! :)
What is the equation of a line that is parallel to -x + 3y = 6 and passes through the
point (3, 5)?
1.y=1/3x + 4
2.y = 3x + 4
3.y = -1/3x-4
4.y = -3x - 4
Answers
Answer:
Two lines are parallel if and only if they have the same slope.therefore the original line y=1/3x+2
so option 1 is the answer
Andrew is showing his work in simplifying -4.5 + 4.2 + 5.6 - 7.3. Identify
any errors in his work or in his reasoning. Write feedback to Andrew
explaining the mistake he made and how to correct his work.
Answers
Answer:
hence the answer for given problem is -2, but andrew get -21.6 which is wrong
Step-by-step explanation:
A fruit stand has to decide what to charge for their produce. They need \$10$10dollar sign, 10 for 4 apples and 4 oranges. They also need $12 for 6 apples and 6 oranges. We put this information into a system of linear equations.
Can we find a unique price for an apple and an orange?
Answers
Answer:
no
Step-by-step explanation:
The prices are inconsistent, so there is no unique price that can be set for either an apple or an orange that will give the total prices indicated.
__
The first relation can be written as ...
$10 = 4A +4O
$10 = 4(A +O) . . . . factor out 4
$2.50 = A +O . . . . divide by 4
The second relation can be written as ...
$12 = 6A +6O
$12 = 6(A +O) . . . . factor out 6
$2 = A +O . . . . . . . divide by 6
These two relations give different prices for 1 apple and 1 orange. There is no price that can be set for either fruit that will give this result.
No unique prices can be assigned.
Which is the graph of y = [X] - 2?
Answers
Answer:
Top right graph
Step-by-step explanation:
Graph is in attached image.
Write the following expression without negative exponents and without parentheses.
(9x)^-1
Answers
Answer:
1/9x
Step-by-step explanation:
The parenthesis around the 9x means that the -1 exponent goes to the whole thing (the 9x) To "fix" a negative exponent push the 9x across a fraction bar to make the exponent positive. When you push the 9x down across a fraction bar that leaves a 1 on top of the fraction, that has nothing to do with the 1 exponent. Its a 1 on top because when you push the 9x down there is nothing left on top so it is a 1.
(9x)^-1
= 1/9x
To be clear, this is a 1 one top and a 9x on the bottom of a fraction.
45°
x 100°
y = [? ]º
Answers
Answer:
55
Step-by-step explanation:
For the first 6% of Bianca's salary, her employer matches 100% of her 401(k)
contributions, and from 6% to 12%, Bianca's employer matches 50% of her
401(k) contributions. Bianca's salary is $50,000, and last year, she contributed
$6000 to her 401(k) plan. What was her employer's contribution to the
401(k)?
OA. $7200
OB. $4500
OC. $6000
OD. $3000
Answers
Answer:
B
Step-by-step explanation:
6% of her salary is .06 * 50000 = 3000 <===== matched 100%
from 6- 12% is another 3000 <=====matched 50% = 1500
3000 + 1500 = 4500 dollars matched
(she put in 6000 and her employer put in 4500 = 10500 total)
How should this model be completed to represent 605 ÷ 18?
Answers
Answer:
Check the attached image
I NEED THIS ANSWER FAST PLEASE
Fill in the missing coordinates of the x-intercept of the line defined by the equation y = x – 4
Answers
Answer:
the answer might be (-4,0) for x coordinates
Find the value of each trigonometric ratio. 18) cos X Y 24 24 25 24 A) C) 25 B) D) 24 25 25
Answers
Answer:
Step-by-step explanation:
Nell is analyzing a quadratic function f(x) and a linear function g(x) will they intersect
Answers
Solve for x: -24 = 6x
1/4
-4
4
- 1/4
Answers
Answer:
-4
Step-by-step explanation:
[tex]~~~~~-24 = 6x\\\\\\\implies -\dfrac{24} 6 = \dfrac{6x}6\\\\\\\implies x = -4[/tex]
-24 = 6x
=> 6 x = -24
=> x = -24/6
=> x = -4
Hence second option is correct
Just need some help with this question.
A northbound train left at noon. Two hours later, a southbound train left the same station. At five o'clock the two trains were 210 miles apart. Find the rate of each train of the northbound train traveled 10 miles per hour faster than the southbound train.
Answers
The rate of each train of the northbound train traveled 10 miles per hour faster than the southbound train 26 miles per hour.
what is speed?
Speed is the time rate at which an object is moving along a path
Let the speed of southbound train is x miles/hour
so, northbound train has speed of x+10 miles/hour.
then, Speed of both train = Total distance/ total time
(x+10+x)=210/5
2x+10= 210/5
2x+10= 42
2x= 32
x= 16 miles per hour (southbound train)
northbound train: 16+10=26 miles per hour
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What is the total number of different 9-letter arrangements that can
be formed using the letters in the word Projector?
Answers
The table shown below lists the time, in days, that it takes for
a package to be delivered based on its mode of transport and
whether it is international or domestic. Some additional
information is provided.
1. The cost per package by air is $100; by train, $50; by
truck, $10; and by boat, $20.
2. Fragile packages cannot be transported by air.
3. Shipping fragile packages costs an extra $20.
4. Shipping international packages costs an extra $30.
Tim needs to transport a fragile package, and he needs it to
arrive as soon as possible. He is shipping domestic. Which of
the following shipping methods should he use?
Answers
Answer:gotchu g there it is
Step-by-step explanation:
Answer:sike gtf
Step-by-step explanation:
The area of a rectangular shop in the mall is 160 square meters. The perimeter is 52 meters. What are the dimensions of the shop?
Answers
Answer:
width = 10 m
length = 16 m
Step-by-step explanation:
Formula
[tex]\textsf{Area of a rectangle} = wl[/tex]
[tex]\textsf{Perimeter of a rectangle}=2(w+l)[/tex]
(where [tex]w[/tex] is width and [tex]l[/tex] is length)
Given:
Area = 160 m²Perimeter = 52 mSubstituting the given values into the formulae to create two equations:
[tex]\textsf{Equation 1}: \quad wl=160[/tex]
[tex]\textsf{Equation 2}: \quad 2(w+l)=52[/tex]
Rearranging Equation 1 to make w the subject:
[tex]\implies w=\dfrac{160}{l}[/tex]
Substituting expression for w into Equation 2 and solving for [tex]l[/tex]:
[tex]\implies 2\left(\dfrac{160}{l}+l\right)=52[/tex]
[tex]\implies \dfrac{160}{l}+l=26[/tex]
[tex]\implies 160+l^2=26l[/tex]
[tex]\implies l^2-26l+160=0[/tex]
[tex]\implies l^2-10l-16l+160=0[/tex]
[tex]\implies l(l-10)-16(l-10)=0[/tex]
[tex]\implies (l-10)(l-16)=0[/tex]
[tex]\implies l=10, 16[/tex]
According to Equation 1:
If length = 10 m ⇒ width = 16 mIf length = 16 m ⇒ width = 10 mAs width < length, the dimensions of the shop are:
width = 10 mlength = 16 mGiven matrix A below, and that A = B, find the value of the elements in B.
A =
9 −2 3
2 17 0
3 22 8
b11 =
9
b12 =
17
b13 =
b21 =
b22 =
b23 =
b31 =
b32 =
b33 =
Answers
The value of Matrix B = [tex]\left[\begin{array}{ccc}9&17&3\\2&17&0\\3&22&8\end{array}\right][/tex]
Given : Matrix A = Matrix B
matrix A= [tex]\left[\begin{array}{ccc}9&-2&3\\2&17&0\\3&22&8\end{array}\right][/tex]
The matrix A= [tex]\left[\begin{array}{ccc}9&-2&3\\2&17&0\\3&22&8\end{array}\right][/tex] (according to the question)
Since it is given A=B
and substituting the given values of elements of B
matrix B=[tex]\left[\begin{array}{ccc}9&17&?\\?&?&?\\?&?&?\end{array}\right][/tex]
According to the property of equality of matrices,
When the matrices are given to be equal, their corresponding elements are also equal
so
b13 = 3
b21 = 2
b22 = 17
b23 = 0
b31 = 3
b32 = 22
b33 =8
Substituting the found out values in place of the question marks,
Matrix B = [tex]\left[\begin{array}{ccc}9&17&3\\2&17&0\\3&22&8\end{array}\right][/tex]
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Answer:
b11 =
9
b12 =
-2
b13 =
3
b21 =
2
b22 =
17
b23 =
0
b31 =
3
b32 =
22
b33 =
8
Step-by-step explanation:
Prove that for a triple element x, y, z the distributive law is always satisfied if one of the elements equals 0 or 1, or if two of the elements are equal.
Answers
The distributive law is satisfied if the numbers 1,2, and 3 are used as multyplying factors.
What is the distributive law?This is basic mathematical law that states:
A multiplied by (b+c) equals (a x b) + (a x c)Is this law satisfied if there are three numbers involved?The law is always satisfied if one of the numbers is 1. Here is an example
2 x (1+2+3) = 2 x 6 = 12or
(2x1) + (2x2) + (2x3)2+4+6 = 12Learn more about mathematical laws in: https://brainly.com/question/15190681
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For 95% of all randomly selected samples of n = 130 students, the mean amount of sleep will be between? Use the empirical rule.
Answers
For 95% of all randomly selected samples of n = 130 students, the
amount of sleep will be between [tex]P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\\\[/tex].
What is the empirical rule?According to the empirical rule, also known as the 68-95-99.7 rule.
The percentage of values that lie within an interval with 68%, 95%, and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
For 95% of all randomly selected samples of n = 130 students, the
amount of sleep will be between can be
[tex]P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\\\[/tex]
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Tracie ran a total of 5 3/4 miles on Saturday and Sunday. She ran 1 5/8 miles on Saturday. how many miles did Tracie run on Sunday?
Answers
let's firstly convert the mixed fractions to improper fractions and then get their difference.
[tex]\stackrel{mixed}{5\frac{3}{4}}\implies \cfrac{5\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{23}{4}} ~\hfill \stackrel{mixed}{1\frac{5}{8}}\implies \cfrac{1\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{13}{8}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Saturday and Sunday}}{\cfrac{23}{4}}~~ - ~~\stackrel{Saturday~only}{\cfrac{13}{8}}\implies \cfrac{(2)23~~ - ~~(1)13}{\underset{\textit{using this LCD}}{8}}\implies \underset{Sunday~only}{\cfrac{33}{8}\implies 4\frac{1}{8}}[/tex]
Solve the radical equation.
√x − 1 + 5 = 9
Answers
Answer:
17
Step-by-step explanation:
square root of x-1 +5=9
square root of x-1 = 4multiple by power of 2 because square root is cancled by 2.
x-1=16,x=17
WHO LOVES AMY WINEHOUSE??
Answers
Answer:
:
Step-by-step explanation:
what are the prime factors of 30
Answers
Step-by-step explanation:
Stay safe, stay healthy and blessed.Have a good day !Thank you♡ #jennifer ♡
Help please and thank you
Answers
Answer: 9
Step-by-step explanation:
By the geometric mean theorem, [tex]\frac{x}[6} =\frac{6}{4} \longrightarrow x=\left(\frac{6}{4} \right)(6)=\boxed{9}[/tex]
A toy rocket is shot vertically into the air from a launching pad 6 feet above the ground with an initial velocity of 88 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=−16t*2 + 88t +6. How long will it take the rocket to reach its maximum height? What is the maximum height?
Question content area bottom
Part 1
The rocket reaches its maximum height at ? second(s) after launch.
Answers
Answer:
Step-by-step explanation:
A short road trip took Susan about 2 hours, traveling at an average speed of 51
miles per hour. Let t represent time (in hours) and r represent speed (in miles per
hour). Identify the type of variation, determine the number of miles she traveled,
and write an equation to represent the relationship between time and speed for
her trip.
Answers
The type of variation between the speed and time is inverse.
The equation is r = d / t
The number of miles travelled is 102 miles.
What is the type of variation?
When the speed a person is driving at increases, the time it takes to travel would decrease. On the hand, speed a person is driving at decreases, the time it takes to travel would increase. This means that there is an inverse relationship.
The equation that represents an inverse relationship is
r = d / t
Where d is the distance
Distance = t x r
51 x 2 = 102 miles
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